Funny enough, this is a case of getting the right thing by accident.

dont = of which; that is, it goes with de and is equivalent to duquel, not à / auquel.

But luckily, we say discuter de quelque chose, not à, so dont works.

However, it’s actually savoir that’s a little unusual here. There aren’t many things you can use as direct objects for savoir. One of them is faits (facts), but not opinions.

The two best options are to replace savoir with connaître, following this frequency chart:

Je connais les opinions dont les gens discutent.

Or rephrase so that what you savoir is the "which" rather than the opinions:

Je sais de quelles opinions les gens discutent.